Small guns like my Seacamp .32 is like carrying a pocket knife! It backs up my .45 some of the time. It is not just about having a second gun, but a backup as the name implies! Your gun jams or is taken from you, you are wounded and lose the use of the arm holding your primary, you need to give your wife a gun to protect herself in a random shooting incident at an eatery, mall, etc...
It is a good idea on some days, and not on others. Cops are not paranoid, and they actually do face people everyday of their career facing who are ACTUALLY out to get them! Imagine getting up everyday, all year, for your whole working career knowing that today could be the day. It NEVER GOES AWAY, as you bury friend after friend! It is not like watching cop shows on TV, and then trying to copy them. In the real world trouble can find you all my itself ... trust me!